List of top Questions asked in CUET (UG)

The number of phone calls (in thousands) are made by a telephone company for five weeks as given below:

Week	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)
No. of Telephone calls	\(110\)	\(130\)	\(93\)	\(104\)	\(211\)

Taking a period of moving averages as 3 weeks, the graph of moving averages can be depicted directly as :

The mean and variance of a Binomial distribution are \(4\) and \(\frac43\) respectively, then the value of \(P(X\geq1)\) is:

The probability distribution of a discrete random variable \(X\) is given below :

\(X\)	\(2\)	\(3\)	\(4\)	\(5\)
\(P(X)\)	\(\frac5k\)	\(\frac7k\)	\(\frac9k\)	\(\frac{11}{k}\)

then the value of k is:

Which of the following can be the probability distribution of a random variable ?

An open box with square base is to be made out of a given quantity of cardboard of area \(P^2\) sq. units. The maximum volume of the box is :

Maximum slope of the curve \(y = -2x^3 + 6x^2 + 5x - 20\) is:

The demand function for a certain product is such that\(P(x) = 3x^2 - x + 200\), where \(x\) is the number of units of the product demanded and \(p(x)\) is the price per unit. Marginal revenue when 10 units are sold is:

A doll making small-scale unit calculates the variable cost of making x number of dolls per day as three times the square of \(x\). The fixed cost of packaging x dolls is  \(₹ 2800\). The marginal cost of producing 120 dolls:

Match List - I with List - II.

List - I	List -II
(A) Null Matrix	(I)\(P(A)+P(B)\)
(B) Scaler Matrix	(II)\(P(A)+P(B)-2P(A\cap B)\)
(C) Skew-symmetric matrix	(III)\(P(B)-P(A\cap B)\)
(D)Symmetric Matrix	(IV)\(P(B)-P(A\cap B)\)

Choose the correct answer from the options given below:

If A and B are symmetric matrices, then which statements are correct?
(A) \((A-B)' = B' - A'\)
(B) \((AB+BA)\) is symmetric matrix
(C) \((AB)'= B'A'\)
(D)\( A'B' = B'A'\)
(E)\( (AB-BA) \)is skew symmetric matrix
Choose the correct answer from the options given below:

If \( \frac {2-x}{4}-\frac{4+x}{6}\geq10 \) then :

\((6:30+19:50), \)in 24 hours clock is :

If \(\frac{x+y}{x-y}+\frac{x-y}{x+y}=\frac{10}{3}\),then \(\frac xy=\)

The mean of Binomial distribution \(B(4,\frac13) \) is : 

The coordinates of the foot of the perpendicular drawn from origin to the plane \(2x - 3y + 4z - 6 = 0\) is :

The area of the region \(\{(x, y) : x^2 + y^2 \leq 2ax, y^2 > ax, x \geq 0, y \geq 0\} \text{ where } a > 0\) , is :

If \(I=\int_{0}^{4}  \frac{\sqrt{x}}{\sqrt{x}+\sqrt{4-x}}dx\), then 8\(I\) is:

The value of \(sin^{-1}\frac{12}{13} +cos^{-1}\frac45+tan^{-1}\frac{63}{16}\) is :

In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs none is defective, is :

Anita and Bikram are two students. Their chances of solving a problem correctly are \(\frac13\) and \(\frac14\) respectively. If their probability of making a common error is  \(\frac{1}{20}\) and they both obtain same answer then the probability that their answer is correct, is :

Objective function \(z=30x-30y \) is subject to which combination of constraints, with feasible solution shown in the figure.

(A)\(x \geq 0, \quad y \geq 0, \quad x \leq 15\)
(B)\(y \leq 20, \quad x + y \leq 30\)
(C)\(x + y \leq 30, \quad x + y \leq 15, \quad 2x - y \leq 5\)
(D)\(2x + y \leq 30, \quad x + y \leq 15, \quad x > 15\)
(E)\(3x + y \leq 30, \quad x + 3y \leq 15, \quad y \geq 20\)
Choose the correct answer from the options given below:
 

Corners points of the feasible region for an LPP are \((1, 1)(2, 0) (3, 1)(\frac32,4)\) and \((0,5)\).Let \(z = px + 4y\),  be the objective function. If maximum of z occurs at \((\frac32,4)\) and\((3,1)\),then the value of p is : 
 

The lines \(\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-K} \) and \(\frac{x-1}{K}=\frac{y-4}{2}=\frac{z-5}{1} \) are coplanar if :

If the planes \(\overrightarrow{r}.(2\hat{i}-\lambda\hat{j}+3\hat{k})=0\) and \(\overrightarrow{r}.(\lambda\hat{i}+5\hat{j}-\hat{k})=5\) are perpendicular to each other ,then value \(\lambda^2+\lambda \) is :

which is the true of the following ?
(A)Any vector \(\overrightarrow{r}\) in space can be written as \((\overrightarrow{r}.\hat{i})\hat{i}+(\overrightarrow{r}.\hat{j})\hat{j}+(\overrightarrow{r}.\hat{k})\hat{k}\) 
(B)If  \(\overrightarrow{a}\)  is perpendicular to  \(\overrightarrow{b}\)\(|\overrightarrow{a}+\overrightarrow{b}|^2=|\overrightarrow{a}|^2+|\overrightarrow{b}|^2\) 
 
(C)If \(|\overrightarrow{a}|=2,|\overrightarrow{b}|=1 \) and \(\overrightarrow{a}.\overrightarrow{b}=1 \) ,the value of \((3\overrightarrow{a}-5\overrightarrow{b}).(2\overrightarrow{a}+7\overrightarrow{b})\) ia 1
(D) \(\overrightarrow{a}=5\hat{i}-\hat{j}-3\hat{k}\) and \(\overrightarrow{b}=\hat{i}+3\hat{j}-5\hat{k}\), is the angle between \(\overrightarrow{a}+\overrightarrow{b}\) and \(\overrightarrow{a}-\overrightarrow{b}\) is \(60\degree\)
Choose the correct answer from the options given below: